An observer-based vaccination control law for an Seir epidemic model based on feedback linearization techniques for nonlinear systems

S. Alonso-Quesada, M. De la Sen, R. P. Agarwal, A. Ibeas

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14 Citations (Scopus)

Abstract

© 2012 Alonso-Quesada et al. This paper presents a vaccination strategy for fighting against the propagation of epidemic diseases. The disease propagation is described by an SEIR (susceptible plus infected plus infectious plus removed populations) epidemic model. The model takes into account the total population amounts as a refrain for the illness transmission since its increase makes the contacts among susceptible and infected more difficult. The vaccination strategy is based on a continuous-time nonlinear control law synthesised via an exact feedback input-output linearization approach. An observer is incorporated into the control scheme to provide online estimates for the susceptible and infected populations in the case when their values are not available from online measurement but they are necessary to implement the control law. The vaccination control is generated based on the information provided by the observer. The control objective is to asymptotically eradicate the infection from the population so that the removed-by-immunity population asymptotically tracks the whole one without precise knowledge of the partial populations. The model positivity, the eradication of the infection under feedback vaccination laws and the stability properties as well as the asymptotic convergence of the estimation errors to zero as time tends to infinity are investigated.
Original languageEnglish
Article number161
JournalAdvances in Difference Equations
Volume2012
Issue number1
DOIs
Publication statusPublished - 12 Sep 2012

Keywords

  • Nonlinear control
  • Nonlinear observers design
  • Positivity
  • SEIR epidemic models
  • Stability
  • Vaccination

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